A numerical solution of problems in calculus of variation using direct method and nonclassical parameterization

DOI10.1016/j.cam.2010.01.048zbMath1189.65132OpenAlexW2068845242MaRDI QIDQ972740

Mahmoud Mashali-Firouzi, Mohammad Maleki

Publication date: 21 May 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.01.048

zbMATH Keywords

numerical examplesnonlinear programmingdirect methodcalculus of variationLagrange multiplier techniquenonclassical parameterization

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Numerical methods based on nonlinear programming (49M37) Existence theories for optimal control problems involving ordinary differential equations (49J15)

Related Items (6)

On using cubic spline for the solution of problems in calculus of variations ⋮ Pseudospectral methods based on nonclassical orthogonal polynomials for solving nonlinear variational problems ⋮ Adaptive pseudospectral methods for solving constrained linear and nonlinear time-delay optimal control problems ⋮ Optimal and Efficient Auctions for the Gradual Procurement of Strategic Service Provider Agents ⋮ A nonclassical Radau collocation method for nonlinear initial-value problems with applications to Lane-Emden type equations ⋮ Direct solution of a type of constrained fractional variational problems via an adaptive pseudospectral method

Cites Work

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• Solution of problems in calculus of variations via He's variational iteration method
• The use of Adomian decomposition method for solving problems in calculus of variations
• The numerical solution of problems in calculus of variation using Chebyshev finite difference method
• Direct and indirect methods for trajectory optimization
• Orthogonal polynomials - Constructive theory and applications
• Control parametrization: a unified approach to optimal control problems with general constraints
• A Gaussian quadrature procedure for use in the solution of the Boltzmann equation and related problems
• Shifted Legendre direct method for variational problems
• Laguerre series direct method for variational problems
• A Walsh series direct method for solving variational problems
• An application of rationalized Haar functions for variational problems
• Direct solution of nonlinear optimal control problems using quasilinearization and Chebyshev polynomials
• Nonclassical pseudospectral method for the solution of brachistochrone problem
• The use of He's variational iteration method for solving variational problems
• Shifted Chebyshev direct method for solving variational problems
• A Chebyshev technique for solving nonlinear optimal control problems
• A Practical Guide to Pseudospectral Methods
• Calculation of Gauss Quadrature Rules
• Combination of non-classical pseudospectral and direct methods for the solution of brachistochrone problem
• A spectral solution of the Sturm-Liouville equation: Comparison of classical and nonclassical basis sets

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